The big event in the world economy is not the Davos economic forum - which ended at the weekend - but the fact that Alan Greenspan, chairman of the US Federal Reserve, will be attending his last Fed meeting tomorrow before retiring. The man who is often credited with single-handedly steering the US economy through a series of storms to a land of sustained growth will be handing over after 18 years at the helm to a respected, but inevitably less experienced, successor. Europe has more than a passing interest in this. Since the eurozone seems unable to generate growth on its own, it is disproportionately reliant on trade generated by US expansion and so has good reasons to be nervous about what will happen next.

Even his critics admit that Mr Greenspan is a giant whose skill, insights and legendary attention to detail have been one of the main forces behind the success of the US economy, even if the last quarter of 2005 suggests a slowing down. Within weeks of taking over in October 1987 he had to contend with the collapse of the stock market. In 1990-91 there was an economic recession followed by the dotcom bubble of the mid-90s, the Russian debt default in 1997, the near-collapse of the LTCM hedge fund in 1998 followed by September 11, hurricane Katrina and the soaring price of oil.

Mr Greenspan even turned failure into success. When he famously warned the stock markets of "irrational exuberance" in December 1996 and they ignored him he rationalised this into a principle: that central banks can't burst bubbles, but merely follow afterwards with a shovel (a theory to which his successor Ben Bernanke also subscribes to). This is not easy for the man in the street to grasp: it suggests that economists are impotent at times when investors are bidding up assets to levels that practically everyone thinks are unrealistic.

This is relevant now because Mr Greenspan's legacy includes three unresolved problems that make it hard to pass final judgment on his tenure. The first is the current UK-style boom in house prices. So far it has been benevolent, feeding consumption and adding to the feel-good factor. It remains to be seen whether it is followed by a sharp drop that could hit consumer spending hard and cause a recession with international repercussions. The other two problems are the huge twin deficits on trade and the budget. Critics have been predicting doomsday scenarios that have not happened for so long that they don't merit headlines any more. But that doesn't mean the risks are not real. Only last week Rachel Lomax, deputy governor of the Bank of England, warned that the US trade deficit and other large global imbalances could have "significant impact on economic activity". That is Bankspeak for saying that if there is a sharp fall in the dollar then don't say we didn't warn you.

It is too early to make a final judgment on him, but there is no doubt that Mr Greenspan's proactive approach to interest rates - he has changed them far more than his European counterpart and is expected to announce another rise tomorrow - has been beneficial. He has been as concerned about encouraging growth as about constraining inflation. And he has done very well on both. He has presided over a remarkable resurgence of productivity since the mid-90s which is the envy of Europe (though, curiously, there has not been a corresponding increase in real wages of a kind that happened in the UK without the productivity increases). One of Gordon Brown's big ambitions is to reproduce a US productivity miracle here. Meanwhile, Mr Greenspan's admirers wonder what would have happened to stagnant eurozone growth if he had been in charge of Europe's central bank. This is another way of saying that, whatever the future has in store, Mr Greenspan has proved himself to be a master of his craft and deserves most of the plaudits showered on him.